Threshold query

Dear Forum,

I have a general comprehension question about the threshold input on the K2 solver. If anyone can answer, I'd be very grateful.

Threshold is described as numeric cap for the average "movement" (vSum?).

Is movement an absolute value of the sum vector length (in m) at the average of all nodes or does movement here relate to velocity too?

I.e. Will setting a low threshold give me a lower accuracy for a complex system (which is slow to converge) than for a simple system (which is fast to converge) or will I achieve the same accuracy simply at different speeds of convergence?

I feel like I've already answered my own question... it's not time dependent is it? The whole point of the projected vectors, is that they are indeed just displacement vectors, not velocity vectors?

Thank you very much!

Greg

Replies to This Discussion

Permalink Reply by Daniel Piker on November 11, 2015 at 11:21am

Hi Greg,

It sums the square of the velocity of each of the particles, then divides by the number of particles.

If the result is less than the input value for "threshold" it stops, if not it keeps iterating.

Hope that is clear and answers your question.

In the next release though there will also be the option to use the maximum residual or acceleration as the stopping criterion instead.

In practice using velocity works pretty well, and when it becomes tiny that's usually a reasonable indicator that things have reached equilibrium, but theoretically there is the chance that if the system has a single oscillation mode it mistakes the instantaneous pause at the peak of this swing as the rest configuration and stops things prematurely. Using residual instead avoids this issue.

Permalink Reply by Gregory Quinn on November 11, 2015 at 12:06pm

Yes,

thank you! Ok, so it is a velocity vector. The velocity of the particles however I assume is not affected by the "speed" of the convergence or vice versa... meaning that for the case described above, a given threshold should produce the same level of "accuracy" for a slowly converging system as for a quickly converging system. But I suppose the comparison might be unfair in the first place.

It seems like a silly question now, but thanks anyway.

Permalink Reply by Daniel Piker on November 11, 2015 at 12:23pm

I think it's a reasonable question.

Using the residual is surely the more correct way of doing things.

For many applications though, I felt that the default velocity threshold of 10^-15 was small enough that these distinctions didn't matter, as the results were already well within the numerical accuracy needed for practical purposes.

I can see now though that in cases where things are moving very slowly but steadily towards equilibrium the distinction could perhaps become significant, which is why I will include this option in the next release.

Permalink Reply by Gregory Quinn on May 16, 2016 at 3:02am

Hi Dan,

I'm making reference to VSum and convergence threshold in my paper. Just to clarify is VSum a root mean square value? According to your description above you don't take the root... so would that mean the final VSum is a squared velocity with units m2/s2? Or do you take the root as well?

Thank you!

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